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From the top of a tree on one side of a street the angles of e

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From the top of a tree on one side of a street the angles of elevation and depression of the top and foot of a tower on the opposite side are respectively found to be $α$ and $β$ . If $h$ is the height of the tree, then the height of the tower is:

\frac{h sin ( α + β )}{cos α sin β}

\frac{h sin ( α + β )}{sin α cos β}

\frac{h cos ( α - β )}{cos α cos β}

\frac{h cos ( α + β )}{cos α cos β}

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From the top of a tree on one side of a street the angles of elevation and depression of the top and foot of a tower on the opposite side are respectively found to be

α

and

β

. If

h

is the height of the tree, then the height of the tower is:

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Text solutionVerified

Let

h_{t} + h = H

be the total height of tower.
Let

x

be the distance between tower and tree.

tan β = \frac{h}{x}

tan α = \frac{h _{t}}{x}

Now,

tan α = \frac{h _{t}}{h cot β}

h_{t} = h \frac{tan α}{tan β}

Total height of the tower,

H = h + h \frac{tan α}{t an β}

= \frac{h tan α + h tan β}{tan β}

Substituting for

tan α

and

tan β

we get,

H = h (\frac{sin β cos α + sin α cos β}{sin β cos α})

Hence, option 'A' is correct.

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Question Text	From the top of a tree on one side of a street the angles of elevation and depression of the top and foot of a tower on the opposite side are respectively found to be $α$ and $β$ . If $h$ is the height of the tree, then the height of the tower is:
Answer Type	Text solution:1
Upvotes	150

From the top of a tree on one side of a street the angles of elevation and depression of the top and foot of a tower on the opposite side are respectively found to be α and β. If h is the height of the tree, then the height of the tower is:

Text solutionVerified

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From the top of a tree on one side of a street the angles of elevation and depression of the top and foot of a tower on the opposite side are respectively found to be $α$ and $β$ . If $h$ is the height of the tree, then the height of the tower is: